I/D #2: Unit O: Derive the Special Right Triangles

Inquiry Activity Summary

Derive the 45-45-90 triangle from an square with a side length of 1

Derive the 30-60-90 triangle from an equilateral triangle with a side length of 1

Inquiry Activity Reflection

Something I never noticed before about the special right triangles is where the triangle comes from. I did not know that the 45-45-90 degree triangle came from a square and that the 30-60-90 degree triangle came from half an equilateral triangle. It was interesting to find out that so much can be found with the Pythagorean Theorem.

Being able to derive these patterns myself aids in my learning because if I forget the rules for the special right triangles I will be able to derive them from a square and the equilateral triangle with the side lengths of 1. I also will know how to use the Pythagorean theorem to determine the side and substitute the values for the variable n, so any other multiples of those values can be used.